Fuel Gas Network Synthesis Using Block Superstructure

Fuel gas network (FGN) synthesis is a systematic method for reducing fresh fuel 1 consumption in a chemical plant. In this work, we address the synthesis of fuel gas network using 2 block superstructure originally proposed for process design and intensification (Demirel et.al. [1]). 3 Instead of a classical source-pool-sink superstructure, we consider a superstructure with multiple 4 feed and product streams. These blocks interact with each other through direct flows that connect a 5 block with its adjacent blocks and through jump flows that connect a block with all blocks. The blocks 6 with feed streams are viewed as fuel sources and the blocks with product streams are regarded as 7 fuel sinks. Addition blocks can be added as pools when there exists intermediate operations among 8 source blocks and sink blocks. These blocks can be arranged in a I×J two-dimensional grid with 9 I = 1 for problems without pools, or I = 2 for problems with pools. J is determined by the maximum 10 number of pools/sinks. With this representation, we formulate fuel gas network synthesis problem 11 as a mixed-integer nonlinear (MINLP) problem to optimally design a fuel gas network with minimal 12 total annul cost. We present a real-life case study from LNG plant to demonstrate the capability of 13 the proposed approach. 14


Introduction
Over 40% of the operating cost of a petrochemical plant is attributed to energy consumption [2].
Energy is needed for raw material preprocessing (preheating, purification), separation of products from intermediates or impurities (product refining), and material transportation.There are multiple energy sources that can be exploited in a refinery, such as liquefied petroleum gases, fuel gas, off-gas, etc. [3,4].These energy sources either come from external process raw materials/purchased fuels or from internal process /products/byproducts. Depending on where these fuel sources originate from, they can be divided as fuel from feed (natural gas) or fuel from product (products, byproducts) [5].In 2016, external fuels supplied to refinery industry in the United States mainly consist of natural gas (31%), electricity (5%), purchased steam and coal (1%) [6].About 63% of the energy consumed by the refinery industry comes from byproducts of the refining process for heat and power.These energy sources sometimes may be convertible to each other.For example, fuel gas, produced internally from the distillation columns, crackers and reformers [7], can be converted to other forms of energy such as steam, electricity and heat.Fuel gas accounts for 46% among all energy sources of refinery industry in the United States in 2016 [6].As a result, it contributes most of primary energy sources to refinery energy needs [8][9][10].Fuel gas is often composed of hydrocarbons (methane, ethane, propane and butane), hydrogen, and carbon monoxide, which have large heating values [11].In most cases, these fuels are flared to the atmosphere, which has detrimental effect on the environment [12,13].
Due to the importance of fuel gas and the environment concern of fuel gas emission, many efforts have been made on improving the equipment efficiency [14] or exploiting new energy sources to decrease fuel gas generation and pollution emission [15].Although these works give insights and directions on improving design of equipment and operating conditions, a general and systematic strategy for elucidating the effective utilization of fuel gas is crucial.For example, in a typical fuel gas system, multiple fuel gas sources with different qualities are available for various equipment (sinks).
As a result, effective management of fuel gas flow among fuel gas sources and fuel gas sinks can provide economic benefits for process design by fully utilizing the heating value embedded in the fuel gas.A system level, integration, is required to account for various interactions within the fuel gas system [16,17].
Optimization-based methods enable to address fuel gas network (FGN) synthesis problems, which aims at redistributing the fuel gas at the system level [2,5,18].To this end, Hasan et al. formalized the FGN synthesis problem as a nonlinear programming problem (NLP) considering the integration of fuel gases appropriately though auxiliary equipment (valves, pipelines, compressors, heaters/coolers, etc.) to achieve best utilization of them [5].They posed the FGN problem as a special class of pooling problem which leads a superstructure as shown in Figure 1 involving many practical features such as nonisobaric and nonisothermal operation, nonisothermal mixing, nonlinear fuel-quality specifications, and emission standards.Jagannath et al. [18] extended this work to include the multi-period FGN operation.This FGN design makes dynamic plant operation more robust and helps to reduce capital costs.Nassim et al. [2,19] modified the FGN model introduced by Hasan et al. [5] to include more constraints on addressing environmental issues and developed a novel methodology for grass-root and retrofit design of FGNs.The first step for many optimization-based methods is the construction of a superstructure.
Hence the appropriate selection of superstructure representation method is critical.There are many representations such as state-task-network [20,21], state-equipment-network [21], P-graph [22,23], state-space [24,25] , and unit-port-conditioning-stream (UPCS) approach [26,27].We recently proposed a new superstructure representation method using building blocks for systematic process intensification [1,28,29].The block superstructure has been constructed based on the dissection of various unit operations into fundamental building blocks.Later on, the proposed block-based approach is applied to address process synthesis problems [30].
In this work, we address the optimal synthesis of fuel gas networks using a block superstructure, originally proposed in our previous work for process synthesis and intensification [1,28,30].Since fuel gas network by its definition is a special class of pooling problem, our block representation method can be extended to general pooling problems as well.In this representation, each block The remaining of the article is structured as follows.First, we elaborate the representation of fuel gas network using block-based approach.Next, we present the MINLP formulation for fuel gas network synthesis problem.Finally, we demonstrate the applicability of our approach with one case study from LNG plant.

Block-based Representation of Fuel Gas Network
In this section, we describe how the classic fuel gas network superstructure such as the one proposed by Hasan et al. [5] can be represented using block-based approach [1,30] as a generic tool for designing fuel gas utilization system.First, we illustrate the classical FGN superstructure and analyze the operation involved in synthesizing a FGN.Next, we construct a block superstructure that also can include the same features.We provide block superstructures for fuel gas network with or without intermediate pools which bring additional mixing operations for more economic benefits.
In a classical FGN superstructure (Hasan et.al [5]), shown in Figure 1, there are FS number of fuel gas sources and PS number of fuel gas sinks.The source stream f has the temperature as T f and the pressure as P f .The sink stream p is obtained with temperature range as  As shown in Figure 2b, the mass and energy transfer within the block superstructure is achieved through the direct connecting streams between adjacent blocks and jump connecting streams among all blocks.Direct connecting streams are achieved via inter-block flow F i,j,k,d , which is the flowrate of component k between block B i,j and B i,j+1 when the flow alignment d = 1 (the connecting flow between adjacent blocks is in horizontal direction) or the flowrate of component k between block B i,j and B i+1,j when the flow alignment d = 2 (the connecting flow between adjacent blocks is in vertical direction) .These direct connecting streams can be either positive when the flow is from block B i,j to B i,j+1 for d = 1 (from block B i,j to B i+1,j for d = 2) or negative when the flow is from block B i,j+1 to B i,j for d = 1 (from block B i+1,j to B i,j for d = 2).Also, these direct connecting stream flow across the block boundary between adjacent blocks.When there is no direct connecting stream (F i,j,k,d = 0), the block boundary between B i,j and B i,j+1 (d=1) or between B i,j and B i+1,j (d=2) is identified as completely restricted boundary.The jump connecting streams are depicted by J i,j,i ,j ,k , which is the flowrate of component k from block B i,j to B i ,j , where i and j designate the row number and column number of a different block.Because of this unidirectional feature, J i,j,i ,j ,k is regarded as an jump product withdrawn from B i,j .Similarly, J i,j,i ,j ,k is regarded as an jump feed supplied to B i ,j .
With these direct and jump connecting streams, blocks with multiple inlets and multiple outlets can serve as stream mixers and splitters, respectively.Source block is identified when multiple external feed streams enter into a block and get mixed, while blocks with external product stream are sinks.
Note that splitting of source stream is not regarded as a splitting operation defined in this work because it could be achieved through the splitting fraction z f eed f rac i,j, f of source stream f into block B i,j and thus can be regarded as supplies of multiple source streams with the same specification.
The operation equipment (heaters/coolers, compressors/expanders) is embedded in the block superstructure through auxiliary units.To represent the pressurizing/depressurizing operation, both direct connecting streams and jump connecting streams are assigned with compressor or expander (only one of them would be selected).The inlet pressure for compressors/expanders is block pressure P i,j when direct/jump connecting streams are outlet flow from B i,j .P i,j is also the outlet pressure for movers when direct/jump connecting streams are inlet flow to B i,j .The inlet temperature for these compressors/expanders arranged at outlet streams (F i,j,k,d and J i,j,i ,j ,k ) of B i,j is the block temperature T i,j , which is also the common temperature of outlet streams from B i,j .The heating and cooling operations are achieved through the heat duty Q h i,j and cold duty Q c i,j , which are obtained from the energy balance around block B i,j .
The general block superstructure for FGN synthesis problem developed in of source stream at the sink block B i,j is zero, then there is no connectivity between the source f and the sink p in block B i,j ; source-sink connectivity exists as long as the feed fraction of source stream z f eed f rac i,j, f is nonzero.
Besides, the horizontal connecting streams between adjacent blocks in Figure 3b are also allowed.This additional feature physically indicates the material flowing between two fuel gas sinks.As for the more general case of fuel gas network superstructure, between the sources and sinks layer, there is normally another layer consisting of L number of intermediate pools, as is shown in design problem without the solution challenge.However, when a large-scale problem is considered, the column number of two rows in this two-dimension block superstructure may not be necessarily the same since we can fix the streams in redundant blocks as zero.This fixing ensures that the number of blocks in the first row is only equal to the number of pools assigned in the system and the number of blocks in the second row is equal to the number of sinks.As is discussed above, the block superstructure can be converted from the classical superstructure of fuel gas network.When there is no priori information provided on flow connectivity among sources, pools and sinks, the block superstructure can be constructed by simply setting the row number I and column number J (i.e., J = max{L,PS}), which then involves as many process alternatives as possible.
The benefit for block representation method is on its generic feature that each block follows the same pattern with multiple inlet streams and outlet streams.
To this end, we introduced the block-based representation for fuel gas network synthesis problems.
The illustrative example is on FGN synthesis with or without intermediate pools.We now develop the MINLP formulation for the FGN synthesis problem.

FGN Synthesis Problem Statement
This section gives the formal problem description for FGN synthesis problem using block superstructure.The sets given for this problem are the set  We consider the assumption for this work as constant properties (heat capacity, lower heating value, etc.), continuous steady-state operation, ideal gas condition, adiabatic expansion/compression, and ideal mixing.With this, we now provide the description of a MINLP model for fuel gas network synthesis based on block superstructure.

MINLP Model Formulation for Block-based Fuel Gas Network Synthesis
The main constraints for the MINLP model involve block material balance, flow directions, block energy balance, work calculation and task assignment/logic constraints.The objective of the FGN synthesis is to minimize the total annual cost.

Block Material Balance
The general material balance for each block B i,j considers the material flows of component k , and jump product flow J p i,j,k .Specifically, the material balance relation is presented as follows.
The last four terms in the above relation are obtained though the following constraints.
All variables including M f i,j,k , H p i,j,k , J f i,j,k and J p i,j,k are obtained by summing multiple feeds or multiple products within single block B i,j .The positive continuous variable M i,j,k, f indicates the amount of component flowrate k into block B i,j carried by feed stream f .The amount of component k taken from block B i,j through product stream p is designated by positive continuous variable H i,j,k,p .The material flowrate for component k from block B i,j to B i ,j is J i,j,i ,j ,k .The index i and j indicate row position and column position of a block B i ,j that is different from B i,j .The subset LN(i, j, i , j ) designates the connection between block B i,j and block B i ,j .It should be noted that for jump connecting flow J i,j,i ,j ,k , i = i and j = j so as to avoid remixing in block B i,j .The stream connectivities at the outer boundary of block superstructure are neglected by setting F i=I,j,k,1 = F i,j=J,k,2 = 0 to ensure that the interaction between the superstructure and the environment is only achieved through external feeds and products.
The flowrate M i,j,k, f for each feed f into block B i,j is completely or partially from the overall available amount F f eed f . The distribution of feed stream f is achieved by the feed fraction z f eed f rac i,j, f ≥ 0 in block B i,j .Hence M i,j,k, f can be determined as follows: Typically, headers receiving fuel gas have purity requirement for inlet streams to ensure correct operating conditions of corresponding equipment.This is achieved through the following inequality constraints: Here, the purity range for component k in product stream p is given by y min,prod k,p , y max,prod k,p . The set kp relates the key component k with product stream p with purity specifications.The product stream p have no purity restrictions when it does not appear in set kp.
On top of purity requirement of key component k in product stream p, possible requirement on ratio of different component k in product stream p is also considered. where is the minimum product ratio requirement between component k and component k for product p.
We also impose the demand constraint for product p supplied to different headers: Here, D L p and D U p are minimum required amount and maximum allowed amount for product stream p respectively.Here depending on requirements of different fuel gas sinks, there are no information provided on D L p , D U p or both.In this case, we set D L p = 0 and . Besides, energy demands De p for each product stream p should be satisfied based on the following constraint: where LHV k refers to lower heating value for each component k, which measures energy content per unit mass or volume of pure combustible component.
Furthermore, each product stream should have acceptable limits on other certain specifications including lower heating value (LHV), reverse specific gravity (1/SG).Assuming that all the considered specifications are linearly additive based on mixture composition or have appropriate linear indices, the following constraint is supplied below for each product stream p [5].
Here the parameter q s,k denote the value of specification s for component k, and q min,prod s,p , q max,prod s,p is the acceptable range of specification s for product stream p.Note that the quality specification q s,k is component flowrate-based instead of total flowrate-based, which is considered in the work of Hasan et.al.[5].
To obtain the total flowrate for all streams associated with the block B i,j , we sum all components in each stream.Specifically, we obtain the toal flowrate FP T i,j,d , FN T i,j,d , J T i,j,i ,j , M T i,j, f , and H T i,j,s from the component flowrate for FP i,j,k,d , FN i,j,k,d , J i,j,i ,j ,k , M i,j,k, f , and H i,j,k,s through the following relations.
J T i,j,i ,j = ∑ k∈K J i,j,i ,j ,k , (i, j, i , j ) ∈ LN(i, j, i , j ) With the total flowrate information, we are able to model the splitting operation for achieving identical composition for all outlet streams including direction connecting streams, jump connecting streams and product streams.These relations are expressed through the following constraints: Here the positive continuous variable y b i,j,k refers to the block composition of component k.This block composition has the physical meaning as the composition of component k for all outlet streams from block B i,j .

Flow Directions
The direct connectivity F i,j,k,d among adjacent blocks is a bidirectional flow with its positive component FP i,j,k,d and negative component FN i,j,k,d .Only one of the component is active when the connecting flow F i,j,k,d is chosen to be nonzero.The selection of flow direction is a decision variable, which is achieved through the following binary variable: As a result, the flow direction determination is achieved though the following constraints:

Block Energy Balance
The involved enthalpy terms for block energy balance includes stream enthalpy, feed enthalpy, product enthalpy, external heating/cooling, work energy associated with expansion/compression.
Then the steady-state energy balance for block B i,j is formulated as follows: where, EF i,j,d represents the stream enthalpy carried by the material flow F i,j,k,d in flow direction d, EM i,j is the overall enthalpy brought into block B i,j along with feed streams , EP i,j is overall enthalpy taken away by product streams, EJ f i,j is overall enthalpy carried into block B i,j through jump feed, EJ p i,j is overall enthalpy taken out from block B i,j through jump product, Q i,j represents amount of heat/cold utility consumed in block B i,j , W i,j indicates the amount of work energy added into or withdrawn from block B i,j .These energy flow variables are shown in Figure 5.The stream enthalpy is determined as follows with the information provided on flowrate, component heat capacities and the block temperature.Depending on the flow direction, in flow alignment d = 1, the inlet temperature for block B i,j is either T i,j from block B i,j to B i,j+1 or T i,j+1 from block B i,j+1 to B i,j ; in flow alignment d = 2, the inlet temperature for block B i,j is either T i,j from block B i,j to B i+1,j or T i+1,j from block B i+1,j to B i,j .
where Cp k is the heat capacity of component k.
The enthalpy amount brought into or withdrawn from block B i,j through jump flows are determined as follows: It should be noted that the inlet temperature of jump flow is always the temperature of source block T i,j .Likewise, the feed enthalpy and product enthalpy are determined with the following constraints: The amount of heat/cold utility consumed in block B i,j can be evaluated through the amount of heat introduced into (Q h i,j ) or withdrawn from (Q c i,j ) block B i,j .
The work energy can be also determined by the amount of work added into or taken out of block B i,j , which are denoted as W com i,j for compression and W exp i,j for expansion respectively.The calculation of W com i,j and W exp i,j is explained later in this Section 4.6.
Finally, to prevent condensation in the process integration network and ensure sufficient superheating, the following constraints are supplied for product stream p in block B i,j [5].
(5.15 P i,j 100 ∑ k∈K H i,j,k,p Cp k T i,j ≤ (HDP p + 5 9 (2.33( where parameter MDP p is moisture dew-point temperature and parameter HDP p is the hydrocarbon dew-point temperature for the product p.

Product Stream Assignments and Logical Constraints
We define binary variables for each product stream p at block B i,j to determine whether they are active in B i,j or not: The identification of block as product block is achieved through the following logical relation, which involves product binary variable.
For each block, there are at most one type of product stream present in block B i,j .The logic proposition is illustrated as follows: Each product stream p appears in the block superstructure for at least once so as to ensure the supply of fuel gas header.
The temperature range for block with product stream p is from T min p to T max p .
T min p z product i,j,p ) i ∈ I, j ∈ J, p ∈ PS (41)

Boundary Assignment
The boundary type between adjacent blocks can be either completely restricted or not.If there is no direct connecting stream between adjacent blocks, then the inter-block boundary is identified as completely restricted boundary.The decision of boundary type is achieved through the following binary variable z cr i,j,d .
If boundary between B i,j and B i,j+1 for d=1 (between B i,j and B i+1,j for d=2) is completetly restricted 0 Otherwise According to the definition of completely restricted boundary, the following constraints are supplied to relate flowrate F i,j,k,d with boundary type.

. Work Calculation
The work term W i,j consists of compression work term W com i,j and expansion work term W exp i,j .
Both W com i,j and W exp i,j consist of work components for direct connecting streams (W ), and jump connecting streams (W comp,J f i ,j ,i,j ).Accordingly, We define the positive variable PR F i,j,d to designate the pressure ratio between the block B i,j+1 and B i,j for flow alignment d = 1 or between the block B i+1,j and B i,j for flow alignment d = 2.The calculation of PR F i,j,d is activated when the boundary of block B i,j is not completely restricted at the corresponding flow alignment d (z cr i,j,d =0).Otherwise, the pressure ratio is taken as 1 to avoid the calculation of the pressure ratio.In horizontal direction, the pressure ratio is determined as follows: Here, PR up is taken as the maximum pressure ratio, which is determined as P max /P min .Similarly, in vertical direction, the pressure ratio is determined as follows: For feed stream f , the pressure ratio is taken as the ratio between block pressure P i,j and parameter From these pressure ratio definitions, we calculate the isentropic work on direct connecting streams, feed streams and jump connecting streams.In the horizontal direction, the inlet isentropic work is determined as follows: Here R gas is the gas constant and γ is the adiabatic compression coefficient.η is the adiabatic compression efficiency.Similarly, the isentropic work for a vertical entering stream is calculated as follows: The work terms related to feed streams and jump connecting streams are calculated in a similar way: Here n f s is the adiabatic compression coefficient.

Objective Function
We consider the components of economic objective in the work of Hasan et al. [5] and derive the objective function for the FGN synthesis as follows.
This objective function aims at minimizing total annual cost (TAC).Here parameter UFC f is the unit cost of different source streams, Di f is the unit cost of treatment cost for the remaining source stream, Rev p is the unit profit from excess energy in product stream p. Besides, the parameter π f denotes the unit transportation cost for source stream f .Parameters CC HU , CC CU , CC exp and CC com denote the The third term indicates the transporting cost of source streams.The last four terms refer to overall cost (both capital cost and operating cost) for heaters, coolers, expansion operations and compression operations.

Case Study
In this section, the fuel gas network synthesis problem with two scenarios are presented to demonstrate the application of block superstructure in synthesis of FGN.We consider two cases: case The corresponding network structure is shown in Figure 7b.The optimal network consumes both HPFG and TBOG fully.Since all the blocks in the first row embed the inlet flow for mixing, five pools can be identified.Pool P 1 accepts source stream from TBOG and FFF, which only supply feed to P 1 .To summarize for the case study section, the block-based representation method can effectively handle the fuel gas synthesis problem and the involvement of intermediate pools helps to improve the management of FGN network, which decreases the total annual cost.enable the synthesis of fuel gas network and helps to find novel network design.Note that the block-based representation method is initially proposed for systematic process intensification, and then applied to process synthesis.The application of block-based approach for FGN integration suggests a general framework towards process intensification, integration and synthesis.

Figure 1 .
Figure 1.Superstructure for a fuel gas network proposed by Hasan et.al [5].

Preprints
(www.preprints.org)| NOT PEER-REVIEWED | Posted: 5 February 2018 doi:10.20944/preprints201802.0025.v1Peer-reviewed version available at Processes 2018, 6, 23; doi:10.3390/pr6030023allows multiple fuel gas inlet flows and single product outlet flow (unique composition for different product streams).The blocks with external feeds and external products serve as sources and sinks for fuel gas respectively.The material and energy flow among different blocks are achieved via jump flow streams connecting all blocks with each other and direct connecting streams connecting only adjacent blocks.The involvement of jump flows is a novelty of this work that avoids the utilization of unnecessary intermediate blocks for inter-block connections.Each stream connecting two adjacent blocks are placed with compressors/expanders to adjust the pressure for achieving the sink requirements.Options for supplying extra hot/cold utility are provided to each block for allowing nonisothermal operation.When there is no direct connecting stream, the block boundary between adjacent blocks is regarded as completely restricted boundary.These blocks are collected in a two-dimensional grid to form a superstructure of blocks.We formulate the fuel gas synthesis problem as a mixed-integer nonlinear optimization (MINLP) problem.The model constraints involve mass and energy balance, flow directions, work calculation and logic constraints.The nonlinear terms of the proposed model arise from splitting, energy balances and work-related calculations.

Figure 2 .
Figure 2. Construction of superstructure for fuel gas synthesis problems: (a) Block superstructure illustration.(b) Block interaction through via connecting streams (blue line: jump product from the block B i,j ; red line: jump feed into the block B i,j ; blocks at diagonal positions are ignored for simplicity).

Figure 2
can be reduced to block superstructure with smaller size if the number of intermediate pools is known beforehand.As Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 5 February 2018 doi:10.20944/preprints201802.0025.v1Peer-reviewed version available at Processes 2018, 6, 23; doi:10.3390/pr6030023an illustrative example, we first consider the case without intermediate pools.Knowing certain number of sources and sinks together with their specification and requirement, the classical superstructure is built by connecting each source and sink and shown in Figure 3a.Here all stream heaters/coolers and expanders/compressors are ignored for representation simplicity.As is shown in Figure 3b, we use a 1×N block superstructure to incorporate the classical superstructure.In this case, the column number is directly equal to number of sinks (J = PS).Since there are no intermediate pools, row number I = 1.Each block serves as sink block, from which product streams are withdrawn.Meanwhile, each block could also function as feed block, where multiple types of source streams are fed.Specifically, taking the first sink block B 1,1 as an example, there could be at most FS number of source streams entering this block.The activation of connectivity between sources and sinks could be reflected by the feed fraction z f eed f rac i,j, f of different sources f .If the feed fraction z f eed f rac i,j, f

Figure 3 .
Figure 3. Block representation for fuel gas network problem: (a) Classical superstructure for fuel gas network.(b) Equivalent block superstructure for fuel gas network.

Figure 4 .
Figure 4. Source streams first come into the intermediate pools, where certain operations such as mixing, purifying are executed according to different sink requirements.The outlet streams coming from the intermediate pools are further directed to the sinks or to the other different pools (shown as the blue line in Figure4a).One way to incorporate the general superstructure is to utilize a block superstructure with larger size so that pools (involving mixing and splitting operations) can be included into the system.With this new feature of intermediate pools, the updated block superstructure is shown in Figure4b.The first row consists of L number of pool blocks and the second row consists of PS number of sink blocks.In this case, the number of columns can be taken as J = max{L, PS}.The existence of intermediate pools make the row number as I = 2, one row to accommodate pools and another row for sinks.The distribution of source streams into each pool blocks is achieved through splitting operation of source streams.In the first row, the jump products are withdrawn from each block as outlet streams of intermediate pools.Specifically, taking the first column of block superstructure in Figure4bas an example, the jump product J P 1,1,k (the summation of all the jump connecting streams to other blocks from block B 1,1 ) is withdrawn and directed to other blocks as jump feeds.These jump feeds (from J 1,2,2,1,k to J 1,J,2,1,k ) are mixed in the second row at sink blocks and then taken as the final product H p 2,1,k (the overall component flowrate for all product stream p).When the number of sources, sinks and pools in the system is not that large, the current commercial solver could handle the FGN

Figure 4 .
Figure 4. General superstructure for fuel gas network synthesis problem with intermediate pools: (a) General superstructure for fuel gas network with intermediate pools.(b) equivalent block superstructure.
for quality s.The objective is to synthesize a fuel gas network that systemically utilizes the arrangement of fuel gas resources and minimizes the total annual cost.The set D = {d|d = 1, 2} designates the flow alignment.The flow alignment d = 1 when the stream is flowing in the horizontal direction, i.e., from block B i,j to B i,j+1 ; d = 2 when the stream is flowing in the vertical direction, i..e., form block B i,j to B i+1,j .The temperature range and flowrate range for all connecting flows including direct connecting flow and jump connecting flow is set as T min , T max and FL, FU respectively.Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 5 February 2018 doi:10.20944/preprints201802.0025.v1Peer-reviewed version available at Processes 2018, 6, 23; doi:10.3390/pr6030023

Figure 5 .
Figure 5. Illustration of energy balance on block B i,j .

Preprints
(www.preprints.org)| NOT PEER-REVIEWED | Posted: 5 February 2018 doi:10.20944/preprints201802.0025.v1Peer-reviewed version available at Processes 2018, 6, 23; doi:10.3390/pr6030023unitcost of heaters, coolers, expansion operations and compression operations, respectively.The first term in the objective function consists of source stream purchase cost and disposal cost.The second term corresponds to the profit gained from the released excess amount of energy in product stream p.

P 2
takes part of stream from source HPFG.P 3 blends streams from EFG and TBOG.Part of external stream from EFG and HPFG enter pool P 4 while P 5 only takes stream from source TBOG.The outlet flow from pool P 1 is distributed into sink C 1 , C 2 and C 4 .The outlet flows from pool P 2 and P 4 are directly transported to sink C 5 .Sink C 2 , C 3 and C 4 accept inlet flow withdrawn from pool P 3 .Part of the outlet flow from pool P 5 is recycled back to pool P 4 and another is transported into sink C 3 .Part of product streams from C 2 and C 1 are recycled back to C 1 and C 5 .The utilization of EFG in the whole FGN network is only 4.51% and the rest of it goes to flare.

Figure 7 .
Figure 7. Block representation and process flowsheet for the optimal solution of FGN with intermediate pools: (a) Block representation for the optimal solution of FGN.(b) process flowsheet for the optimal solution of FGN.

Preprints
(www.preprints.org)| NOT PEER-REVIEWED | Posted: 5 February 2018 doi:10.20944/preprints201802.0025.v1Peer-reviewed version available at Processes 2018, 6, 23; doi:10.3390/pr60300236.ConclusionsWe present an abstract superstructure representation for FGN synthesis, which is based on a block-based arrangement of source and sink.Each block allows multiple external fuel gas source streams and single fuel gas sink streams.The direct connecting streams between adjacent blocks and jump connecting streams among all blocks enable many alternative ways of flowing the mass and energy from sources to sinks.The blocks with multiple inlet streams serve as mixers and the blocks with multiple outlet streams are splitters.These blocks form a superstructure when arranged in a two-dimensional grid.The row number is determined by the number of intermediate pool layers and the number of sink layers.The column number is determined by the number of intermediate pools and the number of sinks.With the representation method, a MINLP model for fuel gas synthesis problem was proposed with constraints on material balance, energy balance, flow directions, and work calculation.A case study from LNG plant was presented for two instances: one without intermediate pools and another with intermediate pools.It was shown that the fuel gas network with pools could significantly reduce the total annual cost by 1.22%, compared to the fuel gas network without intermediate pools.These case study revealed that the block-based representation method would

Table 1 .
[5]hough the definition of fuel gas network is taken from the literature (Hasan et al.[5]), the model we utilized in this work is not based on the total flowrate but the component flowrate.Because of the model discrepancy, we keep part of the source data from the literature in Table1and update required component parameters in Table2.The sink data is directly taken from the literature without any changes and listed in Table3.It should be noted that all the data have been converted to standard units.Sources streams specifications.